re:microtemperament

Hello Paul,

--- In tuning@y..., "Justin White" <justin.white@d...> wrote:
>>
>>
>> Dave wrote
>> <I think maybe I missed your point. What is it you would have me
stop
>> doing, or do differently?>
>>
>> I'm only concerned that newcomers may perhaps not even bother
investigating the
>> riches that JI and [electronic] harmonic timbres for themselves as
a noted
>> tuning authority considers JI and [electronic] harmonic timbres to
be "boring".

>Well then you should be really angry at the "nutty professor", and
>not at Dave Keenan, of all people, who gave us the rotating JI
>dekany, among other riches.

I'm not angry at any one.

Mcl. despte being pretty obnoxious is pretty good for the microtonal community
though. I don't really agree with his ideas re. JI etc [but that is a whole new
can of worms !] I have already stated that I think what Dave is doing is
brilliant.

I am in fact interested in how Daves developments could be applied to a CS
[periodiciy block ?] that I came up with last weekend.

! CS FROM B&C BLUE MATRIX [JUSTIN WHITE].scl
!
SCALE ONLY HAS FOUR INTERVAL SIZES IS PSEUDO MOS
29
!
25/24
135/128
35/32
10/9
9/8
7/6
32/27
6/5
5/4
81/64
21/16
4/3
27/20 or 25/18
45/32
35/24
189/128
3/2
25/16
405/256
105/64
5/3
27/16
7/4
16/9
9/5
15/8
243/128
63/32
2/1

I was contemplating using standard tuning but pythagoran with A=1/1
i.e

E A D G B E
3/2 1/1 4/3 9/8 16/9 3/2

I guess I'd like to know what benefits a microtempered version of this scale
could offer me. I am flexible as to the runing of the strings as well.

How about it Dave ?

>> I have heard guitar technicians say that guitar players can adjust
intonation
>> via finger pressure. Does this mean that microtemperament or
strictly just will
>> sound the same and be always just in the hands of a player with a
good ear ?

>Justin, wouldn't it be valuable to distinguish between "Strict JI"
>and "Adaptive JI" in discussions like this? As I understand your
>philosophy, Justin, you're interested in a form of strict JI that
>Dave isn't even considering here. Sure, a microtempered guitar can
>easily play vertical JI chords in the hands of a skilled player. Even
>a 12-tET guitar can do that. But then we're dealing with adaptive JI
>(which I favor anyway), rather than strict JI, where _all_ the
>intervals, melodic and harmonic, are based on ratios. Justin, from
>your comments, I take it you're interested in strict JI -- yes?

You would only get strict JI on a guitar from a robot who could play with
uniform finger placement and pressure. My ideal is for strict JI in referential
melody and harmony bending [barbershop style] to be consonant. I'm not sure this
meets your definition of adaptive tuning [which I think is close to John de
Laubenfels approach]. But practically speaking ideals are not always the most
advantageous option to pursue. There is of course the aspect of acuity in
melodic listening being much less precise than in harmony.

Justin White

--- In tuning@y..., "Justin White" <justin.white@d...> wrote:

> I am in fact interested in how Daves developments could be applied
to a CS
> [periodiciy block ?] that I came up with last weekend.
>
> ! CS FROM B&C BLUE MATRIX [JUSTIN WHITE].scl
> !
> SCALE ONLY HAS FOUR INTERVAL SIZES IS PSEUDO MOS
> 29
> !
25/24;
135/128;
35/32;
10/9;
9/8;
7/6;
32/27;
6/5;
5/4;
81/64;
21/16;
4/3;
25/18; (this is better than 27/20)
45/32;
35/24;
189/128;
3/2;
25/16;
405/256;
105/64;
5/3;
27/16;
7/4;
16/9;
9/5;
15/8;
243/128;
63/32;
2/1;

This has unison vectors

48:49 [1 0 -2]
225:224 [2 2 -1]
32805:32768 [8 1 0]

This matrix indeed has a determinant of 29.

If we temper out 225:224 and 5120:5103, yours becomes a scale with
two step sizes

LsLssLssLsLsLsLssLsLssLssLsLs

This is not an MOS but is tetrachordal in many modes:

LsLssLssLsLs LsLss LsLssLssLsLs
|----4:3-----| |----4:3-----|

sLssLssLsLsL sLssL sLssLssLsLsL
|----4:3-----| |----4:3-----|

LssLssLsLsLs LssLs LssLssLsLsLs
|----4:3-----| |----4:3-----|

ssLssLsLsLsL ssLsL ssLssLsLsLsL
|----4:3-----| |----4:3-----|

sLssLsLsLsLs sLsLs sLssLsLsLsLs
|----4:3-----| |----4:3-----|

LssLsLsLsLss LsLss LssLsLsLsLss
|----4:3-----| |----4:3-----|

ssLsLsLsLssL sLssL ssLsLsLsLssL
|----4:3-----| |----4:3-----|

sLsLsLsLssLs LssLs sLsLsLsLssLs
|----4:3-----| |----4:3-----|

LsLsLsLssLsL ssLss LsLsLsLssLss
|----4:3-----| |----4:3-----|

etc.

but not all:

sLsLsLssLsLssLssLsLsLsLssLssL

The Fokker periodicity block though, when so tempered, with the
origin at a particular corner, leads to this MOS:

LsLssLsLssLsLsLssLsLssLsLsLss (compared to yours which was
LsLssLssLsLsLsLssLsLssLssLsLs -- three chromatic alterations)

The generator of this scale is the perfect fourth, so I think the
scale is omnitetrachordal. Its ideal temperament should already be in
Graham's list -- one of the schismic 7-limit ones. When untempered,
it's:

0 1 1
62.961 28 27 (224:225 comma : your 25/24)
92.179 135 128
155.14 35 32
182.4 10 9
203.91 9 8
266.87 7 6
294.13 32 27
359.05 315 256 (512:525 chroma : your 6/5)
386.31 5 4
407.82 81 64
470.78 21 16
498.04 4 3
562.96 2835 2048 (5103:5120 comma : your 28/15)
590.22 45 32
653.18 35 24
674.69 189 128
701.96 3 2
764.92 14 9 (224:225 comma : your 25/24)
794.13 405 256
857.09 105 64
884.36 5 3
905.87 27 16
968.83 7 4
996.09 16 9
1061 945 512 (512:525 chroma : your 6/5)
1088.3 15 8
1151.2 35 18 (2240/2187 chroma : yours
1172.7 63 32

Note that

2240:2187 / 49:48 = 5103:5120;
5103:5120 / 32768:32805 = 225:224

525:512 / 49:48 = 225:224

>
> I guess I'd like to know what benefits a microtempered version of
this scale
> could offer me.

I don't have time to go through it all now, but it's clear you'll
get "extra" consonant intervals and chords if you tune L and s in
your scale according to their sizes in the 29-tone MOS of Graham's 7-
limit schismic generator (who can give L and s)?

You'll get even more if you use the MOS itself rather than your scale
which has three chromatic alterations -- and the MOS is
omnitetrachordal here (right?)

I wrote,

>48:49 [1 0 -2]
>225:224 [2 2 -1]
>32805:32768 [8 1 0]

>This matrix indeed has a determinant of 29.

>If we temper out 225:224 and 5120:5103

oops -- I meant if we temper out 225:224 and 32805:32768 -- which
actually amounts to the same thing, but why confuse you?

Justin White wrote:

>I am in fact interested in how Daves developments could be applied to a CS
>[periodiciy block ?] that I came up with last weekend.

I'll assume you will treat it as 9-limit. i.e. I'll assume you won't be
depending on any ratios of 15 being just.

If you were to make it MOS (without adding notes) it would be in schismic
temperament (497.8 c generator) but that would have a 9-limit error of 4.3
cents. If this was acceptable it would make a guitar with very few missing
notes and you might even keep the standard EADGBE open tuning without too
much loss. To make the math easier you could consider it a subset of 94-EDO
and have the errors only go up to 4.7c. But I'll assume that even 4.3c is
too much.

We could try 9-limit Kleismic at 2.7c, or Miracle at 3.3c. Let's go for
9-limit Kleismic (316.8c generator). I haven't worked with that before.
It's one of Graham Breed's recent discoveries. From Grahams file
http://x31eq.com/limit9.txt
we get the mapping from primes to numbers of generators
3-> 6 gens
5-> 5 gens
7->22 gens

Then we can map your scale to numbers of generators by first
prime-factorising the ratios. I do all this in Excel. I put in both 27/20
and 25/18 for now. Then we mark all the notes on a chain of generators, and
we see how many notes we lose from our scale if we shift the pattern by 1
generator then 2 generators etc. From that we find what shifts along the
chain result in the fewest notes lost. These turn out to be (not
surprisingly) +6 and -6 generators (which correspond to 2:3 and 3:4). These
shifts lose only 5 notes. Unfortunately we can't make an open string tuning
with only these (and 0) without having strings either an 8:9 or a 2:3
apart. So we include the second best, which are +-5, +-11 and +-12. These
all lose 10 notes. Now we look at how many ways we can set them up to give
acceptable intervals between open strings, when we take octaves into
account. i.e. ideally we'd only have intervals between a neutral third and
a perfect fourth but are willing to go a little outside those if necessary.

Then we choose a few of these (should really look at them all but not
automated yet) and find the scale rotation for each that loses the fewest
notes in the critical region between the nut and the position corresponding
to the pitch of the next string. I treat this linear temperament as a
subset of 125-EDO to make the process easier (it turns out I could have
used 72-EDO). For the final result I've used the 9-limit RMS optimum
generator 316.744c, even though this raises the max error to 3.0 cents (in
the 4:9).

Here's the best combination of open string tuning and scale rotation I
could find in a day. With this one it turns out to be best to choose 27/20
rather than 25/18. I'm afraid, with only 29 full-width frets, it has 5
notes missing from the critical region, and in the low octave they are
missing completely from the guitar. 16/9, 9/5, 243/128, 1/1, 32/27.

These can of course be restored by adding 5 more frets for a total of 34.
Unfortunately the extra fret for 32/27 introduces a closer fret spacing (in
cents) than already exists. 12.6c versus 18.1c. But it's close to the nut,
so it is no worse in physical spacing than some of the those further down
the neck.

The open strings and intervals between them are:

432.6 383.7 383.7 432.6 383.7 cents
7:9 4:5 4:5 7:9 4:5 approx ratio
7/4 9/8 45/32 7/4 9/8 45/32 note name

The fretting in cents is:

0.0
30.7
48.8
67.0
85.1
97.7
115.8
134.0
182.8
200.9
231.6
267.9
298.6
316.7
383.7
414.4
432.6
499.5
517.7
584.6
615.4
682.3
700.5
767.4
798.1
816.3
883.3
914.0
932.1
999.1
1017.2
1084.2
1114.9
1133.0
1200.0

I've run out of time today to show the layout of the notes on the
fingerboard.
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com

In-Reply-To: <9m4t34+nfo1@eGroups.com>
Paul wrote:

> I don't have time to go through it all now, but it's clear you'll
> get "extra" consonant intervals and chords if you tune L and s in
> your scale according to their sizes in the 29-tone MOS of Graham's 7-
> limit schismic generator (who can give L and s)?

I don't know about the theoretical optimum, but 135-equal works well
enough in practice. L=62.2 cents and s=26.7 cents. Or s (the comma) is
1/45 octaves if you want something easy to remember.

> You'll get even more if you use the MOS itself rather than your scale
> which has three chromatic alterations -- and the MOS is
> omnitetrachordal here (right?)

I use a fourth as the interval of repetition, so I get infinite
omnitetrachordality! At least for conjunct tetrachords.

Graham

Dave,

Wouldn't the great advantages of a schismic temperament for the
guitar layout (standard tuning used virtually intact, no pairs of
frets closer than 26 cents) more than make up for the minor
difference in approximation quality, which is smaller than the
intonational vagaries of a guitar anyway?

I suggest we take the fret spacing on the Dinarra as a lower bound.

-Paul

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> Dave,
>
> Wouldn't the great advantages of a schismic temperament for the
> guitar layout (standard tuning used virtually intact, no pairs of
> frets closer than 26 cents) more than make up for the minor
> difference in approximation quality, which is smaller than the
> intonational vagaries of a guitar anyway?

Well hey it sure would for me. And I did suggest it to Justin. But
this is _his_ JI guitar and I was guessing that 4.3 cents plus the
guitar intonation vagaries is too much, but 2.7+ might be acceptable.

For guitar microtempering purposes the temperament used doesn't need
to have any relationship to the scale being approximated. Except the
same odd-limit.

By the way, Carl, I was wrong. When you add two normal distributions
with the same standard deviation (RMS error) the resulting
distribution has _both_ rms and max-absolute errors typically being
only sqrt(2) times larger. Or more generally
total_err = sqrt(err1^2 + err2^2).

> I suggest we take the fret spacing on the Dinarra as a lower bound.

A good idea. Do you mean in mm or cents? Dinarra minimum is 20.8
cents, so my kleismic proposal for Justin's guitar fails, but only by
a small amount.

-- Dave Keenan

Hello Paul and Dave,

I'd just like to thank for your work so far here.

With the guitar I have four fretboards. I would like to keep 3 of them
strictly just for use as studio instruments [i.e non realtime for
recording along side synths etc.] With the fourth one I would like to
use one of the options you are both presenting.

I am not averse to using the schismic temperament. But I would like to
ear test both [all ?] the options. Could I have some cents values for
the schismic scale ? I think Dave listed the cents values for his
kleismic proposal earlier. Any way I'll have a play and tell you what I
think.

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > Dave,
> >
> > Wouldn't the great advantages of a schismic temperament for the
> > guitar layout (standard tuning used virtually intact, no pairs of
> > frets closer than 26 cents) more than make up for the minor
> > difference in approximation quality, which is smaller than the
> > intonational vagaries of a guitar anyway?
>
> Well hey it sure would for me. And I did suggest it to Justin. But
> this is _his_ JI guitar and I was guessing that 4.3 cents plus the
> guitar intonation vagaries is too much, but 2.7+ might be acceptable.
>
> For guitar microtempering purposes the temperament used doesn't need
> to have any relationship to the scale being approximated. Except the
> same odd-limit.
>
> By the way, Carl, I was wrong. When you add two normal distributions
> with the same standard deviation (RMS error) the resulting
> distribution has _both_ rms and max-absolute errors typically being
> only sqrt(2) times larger. Or more generally
> total_err = sqrt(err1^2 + err2^2).
>
> > I suggest we take the fret spacing on the Dinarra as a lower bound.
>
> A good idea. Do you mean in mm or cents? Dinarra minimum is 20.8
> cents, so my kleismic proposal for Justin's guitar fails, but only by
> a small amount.
>
> -- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > Dave,
> >
> > Wouldn't the great advantages of a schismic temperament for the
> > guitar layout (standard tuning used virtually intact, no pairs of
> > frets closer than 26 cents) more than make up for the minor
> > difference in approximation quality, which is smaller than the
> > intonational vagaries of a guitar anyway?
>
> Well hey it sure would for me. And I did suggest it to Justin. But
> this is _his_ JI guitar and I was guessing that 4.3 cents plus the
> guitar intonation vagaries is too much, but 2.7+ might be
acceptable.
>
> For guitar microtempering purposes the temperament used doesn't
need
> to have any relationship to the scale being approximated. Except
the
> same odd-limit.

But Dave, what about all the "extra" consonances available? Only with
schismic temperament will Justin have access to a slice of the
lattice that is infinite in two dimensions. Perhaps one would want to
temper out only one of the commatic unison vectors (225:224 or
32805:32768 or 5120:5103) and have a planar microtemperament, giving
Justin access to a strip of the lattice that is infinite in one
dimension. But from a tuning perspective, there's no reason you'd
want to use a kleismic or MIRACLE temperament for Justin's tuning.

> A good idea. Do you mean in mm or cents? Dinarra minimum is 20.8
> cents, so my kleismic proposal for Justin's guitar fails, but only
by
> a small amount.

But in the worst place. Next to the nut is the _worst_ place for a
really small interval -- the bending of the string will be maximal
unless the nut is really low, and then you're very susceptible to
buzzing.

--- In tuning@y..., "Justin White " <JUSTINTONATION@H...> wrote:
>
>
> Hello Paul and Dave,
>
> I'd just like to thank for your work so far here.
>
> With the guitar I have four fretboards. I would like to keep 3 of
them
> strictly just for use as studio instruments [i.e non realtime for
> recording along side synths etc.] With the fourth one I would like
to
> use one of the options you are both presenting.
>
> I am not averse to using the schismic temperament. But I would like
to
> ear test both [all ?] the options. Could I have some cents values
for
> the schismic scale ?

I will do this tomorrow, and I will also work out a color 3-D
lattice, so you can see all the extra consonances that schismic
temperament will give you.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> But Dave, what about all the "extra" consonances available? Only
with
> schismic temperament will Justin have access to a slice of the
> lattice that is infinite in two dimensions.

But Paul, Justin really wanted a _just_ tuning (specified in rational
terms)! And doesn't particularly care about improving the near-just
intervals (or didn't until recently). His interest in microtemperament
is/was purely its ability to give a practical fingerboard design for
his JI scale.

>Perhaps one would want
to
> temper out only one of the commatic unison vectors (225:224 or
> 32805:32768 or 5120:5103) and have a planar microtemperament, giving
> Justin access to a strip of the lattice that is infinite in one
> dimension. But from a tuning perspective, there's no reason you'd
> want to use a kleismic or MIRACLE temperament for Justin's tuning.

Yes there is! To keep it sounding as Just as possible while making a
fingerboard practical.

> > Dinarra minimum is 20.8
> > cents, so my kleismic proposal for Justin's guitar fails, but only
> by
> > a small amount.
>
> But in the worst place. Next to the nut is the _worst_ place for a
> really small interval -- the bending of the string will be maximal
> unless the nut is really low, and then you're very susceptible to
> buzzing.

True. But my design does not have the smallest step right next to the
nut. Here are the first few frets again, in cents, with step sizes.

frets steps (cents)
0.0(nut) 30.7
30.7 18.1
48.8 18.1
67.0 18.1
85.1 12.6 (smallest)
97.7 18.1
115.8 18.1
134.0 48.8
182.8

You know, most of this problem could be solved if these exchangeable
fingerboards didn't rely on the nut to give the open string tuning,
but each provided their own _zeroth_fret_, which will end up right
against the (deeply cut) nut.

Is there any reason _not_ to use such zeroth frets?

Of course, they cannot be retrofitted to existing fingerboards, but
would have to be designed in from scratch, since it would require all
the other frets to shift down a bit to maintain the tuning.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "Justin White " <JUSTINTONATION@H...> wrote:
> > Could I have some cents values for the schismic scale ?
>
> I will do this tomorrow,

I assume you'e seen by now that I already did that in
/tuning/topicId_27387.html#27392

> and I will also work out a color 3-D
> lattice, so you can see all the extra consonances that schismic
> temperament will give you.

Great!

-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
<snip>
> You know, most of this problem could be solved if these exchangeable
> fingerboards didn't rely on the nut to give the open string tuning,
> but each provided their own _zeroth_fret_, which will end up right
> against the (deeply cut) nut.
>
> Is there any reason _not_ to use such zeroth frets?
>
> Of course, they cannot be retrofitted to existing fingerboards, but
> would have to be designed in from scratch, since it would require
> all the other frets to shift down a bit to maintain the tuning.

Hi Dave. Actually, for a fixed fingerboard, it is possible and not too
difficult to fit a zeroth fret. Remove the nut and undercut the
fingerboard at the nut like this

___________
\__________~~ but at about 45 degrees. Then a new piece of wood
____________________
can be laid in |________\___________~~~~ and a fret slot and nut

groove cut. Alternately, if you can match the wood, make the undercut
ahead of the nut and lay in the new piece. Of course, whether this is
possible depends on the guitar. I have always felt that a zero fret
was preferable, and in fact I had to eat a bug (a really small one) as
the result of losing a challenge right here on the forum, when I
challenged the readers to give me one good reason why they would
prefer a nut over a zero fret. At least one, I can't remember who,
said they liked having the open strings sound different from the
fretted ones for certain kinds of open chordal playing.

John Starrett

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > But Dave, what about all the "extra" consonances available? Only
> with
> > schismic temperament will Justin have access to a slice of the
> > lattice that is infinite in two dimensions.
>
> But Paul, Justin really wanted a _just_ tuning (specified in
rational
> terms)! And doesn't particularly care about improving the near-just
> intervals (or didn't until recently). His interest in
microtemperament
> is/was purely its ability to give a practical fingerboard design
for
> his JI scale.

Justin simply asked "what would be the benefits of microtemperament".
In my view, the main benefit is getting more consonances, and much
easier access to adjacent portions of the lattice (I'm envisioning a
41-fret-per-octave guitar). Justin, is Dave right that your only
interest in microtemperament is for its ability to give a practical
fingerboard design?
>
> >Perhaps one would want
> to
> > temper out only one of the commatic unison vectors (225:224 or
> > 32805:32768 or 5120:5103) and have a planar microtemperament,
giving
> > Justin access to a strip of the lattice that is infinite in one
> > dimension. But from a tuning perspective, there's no reason you'd
> > want to use a kleismic or MIRACLE temperament for Justin's tuning.
>
> Yes there is! To keep it sounding as Just as possible while making
a
> fingerboard practical.

Well, I said from a tuning perspective, by which I meant, aside from
practical instrument-design considerations.
>
> Is there any reason _not_ to use such zeroth frets?

Some guitars have them -- it's just that nuts give those open string
notes an extra nice tone.
>
> Of course, they cannot be retrofitted to existing fingerboards, but
> would have to be designed in from scratch, since it would require
all
> the other frets to shift down a bit to maintain the tuning.

Huh? If you put the zeroth fret in the right place, then . . .

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@y..., "Justin White " <JUSTINTONATION@H...> wrote:
> > > Could I have some cents values for the schismic scale ?
> >
> > I will do this tomorrow,
>
> I assume you'e seen by now that I already did that in
> /tuning/topicId_27387.html#27392

Thanks. That will save me some work. It should be clear now how a 41-
fret-per-octave guitar, with no frets closer than 26 cents, could
give both Justin's scale _and_ the 29-tone MOS in various keys, and
of course lots of extra consonances . . .
>
> > and I will also work out a color 3-D
> > lattice, so you can see all the extra consonances that schismic
> > temperament will give you.
>
> Great!

I'll get to this right away . . . it will take a while though (still
using Microsoft Paint).

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> > Of course, they cannot be retrofitted to existing fingerboards,
but
> > would have to be designed in from scratch, since it would require
> all
> > the other frets to shift down a bit to maintain the tuning.
>
> Huh? If you put the zeroth fret in the right place, then . . .

I meant, cannot be retrofitted to exchangeable fingerboards that have
already been fretted.

The idea is that the zeroth fret goes with the fingerboard while the
nut of course must stay with the guitar. That way, the distance
between the first fret and the strings (which is what gives the major
buzzing problems) does not depend on the nut or the mechanical
tolerance of fitting the fingerboard to the guitar. It should even
make it practical to exchange fingerboards between (same-model)
guitars.

John, thanks for that idea about retrofitting zeroth frets to fixed
fingerboards. I'll bet Paul just said that about the different sound
to make you eat that bug. ;-)

Incidentally, does anyone know what the theoretical or practical
optimal profile is for a fingerboard (or rather for the line thru the
fret-tops) to give constant amplitude-before-next-fret-buzzing along
with constant finger-force-required, all the way down the neck.
(constant-amplitude). Is it a straight line?

Do folks use shims to pack up the sound-hole/pickup end of these
exchangeable fingerboards to get the action they want?

-- Dave Keenan

<snip>
>
> John, thanks for that idea about retrofitting zeroth frets to fixed
> fingerboards. I'll bet Paul just said that about the different sound
> to make you eat that bug. ;-)

Yup, I bet it was Paul.

> Incidentally, does anyone know what the theoretical or practical
> optimal profile is for a fingerboard (or rather for the line thru
the
> fret-tops) to give constant amplitude-before-next-fret-buzzing along
> with constant finger-force-required, all the way down the neck.
> (constant-amplitude). Is it a straight line?
<snip>
> -- Dave Keenan

There may be an optimal theoretical profile given a particular
player's style and string guage. When I adjust someone's intonation
the first step is to intonate the bridge, then I adjust the neck
relief, neck attitude if it is a bolt on, and bridgepiece height so
that for open chords the strings *just barely* buzz when they are
playing as hard as they ever play. If it is electric I try to have
them play through their amp, since they will play at a natural volume
then. Usually the action is optimal at this point, and I then fine
tune the intonation to accomodate the new string height. For most
folks, the neck has a slight relief at this point, I'd estimate about
3/32 inch at the octave fret for 008 to 036 guage sets on an electric.
More of an art, I'd guess, since different players have different
tolerances for string height to buzz balance. An electric player, for
instance, can usually tolerate more buzz since a little buzz doesn't
sound if your amp's up loud.

John Starrett

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

> Incidentally, does anyone know what the theoretical or practical
> optimal profile is for a fingerboard (or rather for the line thru
the
> fret-tops) to give constant amplitude-before-next-fret-buzzing
along
> with constant finger-force-required, all the way down the neck.
> (constant-amplitude). Is it a straight line?

I don't know about the constant stuff, but the normal set-up for a
guitar neck is very, very slightly concave.